There are some septs in Dorne dedicated to the Faith of the Seven.

Obara touched her whip. “Thousands are crossing the sands afoot to climb the Boneway, so they may help Ellaria bring my father home. The septs are packed to bursting, and the red priests have lit their temple fires.” (AFFC -The Captain of Guards I)

I believe that is the only canon quote we have regarding septs in Dorne. There is no mention of any specific sept in Sunspear.

Interestingly enough, the faith of the Lord of Light seems to be a significant minority in Dorne, significant enough to be mentioned. Where are they in Dorne? We don’t know (yet?).

But the Faith of the Seven is the main religion and has been so for a very long time. Therefore, we can only rightfully assume that septs have been around for centuries in Dorne too. Where would people go to pray otherwise? Arianne even mentions how “she lit candles to the Maid in thanks” (AFFC - The Princess in the Tower). After all, before Nymeria’s arrival, Dorne was made of Andals, the people behind the Faith’s origins and spread. Most of the Rhoynar converted, and those that didn’t became the orphans.

On the day they wed, Nymeria fired her ships, so her people would understand that there could be no going back. Most were glad to see those flames, for their voyagings had been long and terrible before they came to Dorne, and many and more had been lost to storm, disease, and slavery. There were a few who mourned, however. They did not love this dry red land or its seven-faced god, so they clung to their old ways, hammered boats together from the hulks of the burned ships, and became the orphans of the Greenblood. (AFFC - The Queenmaker)

Although we know there are septs, there is no mention of a Great Sept or any kind of hierarchy for septs in Dorne. On the other side of the Red Mountains, King’s Landing has its Great Sept of Baelor. Given that Dorne and the rest of Westeros were separate for two centuries, how did this work? GRRM answered back in 2001 in an entry entitled “Concerning Dorne”.

Before the unification of Dorne with the rest of the Seven Kingdoms, what did they do for a High Septon? Was there an Antipope-type of rival supported by the Martells? An Archsepton of Sunspear? Or did Dorne accept the High Septon, despite being based in King's Landing and beholden to the Targaryens?

GRRM: The Faith is not limited to the Seven Kingdoms proper, any more than the medieval Church was limited to Italy. So no, no Dornish antipopes. And the High Septon was not especially "beholden" to the Targaryens. In fact, he was a dangerous rival... well, until the reign of Maegor the Cruel, at least.

So, no need for a Great Sept from which some kind of religious authority ruled over Dorne. “Regular” septs were enough. This would explain why no sept is mentioned as a chief structure in Sunspear’s layout.